'The difficulty of the course, combined with the unpredictable elements would most certainly expose this physical shortcoming,' the 49-year-old Norman said in a letter to PGA of America president M.S. Orender.
'During my practice round Wednesday, it was obvious that my mind was attempting to make promises my body was unable to keep. By withdrawing, I am giving someone else the chance to compete for the Wanamaker Trophy.'
A story on PGATour.com Thursday says Norman, 49, has made it his swan song. He will probably compete in his Franklin Templeton Shootout in the off-season and possibly the British Open next year. And he may play in a few selected Champions Tour events next year.
'I would say, yes, my PGA Tour career is pretty much done after this week,' Norman told Dave Shedloski.
A degenerative back condition prevents Norman from practicing excessively. And his outside business interests make it unlikely that he would spend hour after hour practicing, even if he were physically able.
Norman has teed it up seven times this year, making only one cut.
'It's an incentive factor with me,' Norman told PGATour.com. 'It's a matter of wanting to get out there and play, and I just dont feel that its in me. I've had my business for 10 years, so that's not really the issue.
'The fact is, I don't know what I want to do, but competitive golf isn't high on my list anymore.'
Norman was No. 1 on the world rankings for 332 weeks - by coincidence, a record that will be tied by Tiger Woods this week.